Unsteady forces on circular cylinders in a cross-flow

A three-axis piezoelectric load cell was used to measure the local unsteady forces induced on cylinders placed in a cross-flow. In conjunction with this, a single hot-wire was used to traverse the wake at a fixed distance behind the cylinder so that correlations between the induced forces on the cylinder and the wake velocity could be calculated to provide insight into the character of the flow-induced unsteady forces. Experiments were carried out on both two-dimensional and finite-span cylinders at a Reynolds number of 46,000. For the two-dimensional cylinder case, substantial evidence was obtained to demonstrate that the strength of the vortex roll-up along the span was quite uniform. Consequently, the lift-velocity correlation along the span remained unchanged. On the other hand, there was a total lack of correlation between the fluctuating drag and the wake velocity, thus indicating that the drag signal was not quite periodic. In the finite-span cylinder case, the separated flow from the top edge of the cylinder was found to suppress vortex shedding along the span of the cylinder, destroyed its coherence and caused the wake flow to oscillate in the stream direction. This oscillation induced a significant fluctuating drag on the cylinder. Consequently, the fluctuating drag far exceeded the fluctuating lift and the wake velocity was found to correlate well with the drag and not with the lift. This correlation remained intact along the span of the cylinder. Finally, the rms fluctuating lift and drag forces were found to vary along the cylinder span, with the lift increasing and the drag decreasing as the base of the cylinder is approached; thus suggesting that a submerged two-dimensional region exists near the base of the cylinder.List of symbols a span of active element on cylinder - C_D local rms drag coefficient, - C_L local rms lift coefficient, - C_D local mean drag coefficient - (C_D)_2D spanwise-averaged mean drag coefficient for two dimensional cylinder - d diameter of cylinder (= 10.2 cm) - D fluctuating component of instantaneous drag - D local rms of fluctuating drag - E_D power spectrum of fluctuating drag, defined as - E_L power spectrum of fluctuating lift, defined as - E_U power spectrum of fluctuating streamwise velocity, defined as - f_L dominant frequency of lift spectrum - f_D dominant frequency of drag spectrum - f_u dominant frequency of velocity spectrum - h span of cylinder - H height of test section (= 30.5 cm) - L fluctuating component of instantaneous lift - L local rms of fluctuating lift - R_Du() cross-correlation function of streamwise velocity and local drag - R_Lu() cross-correlation function of streamwise velocity and local lift - Re Reynolds number, - S_L Strouhal number based on f_L, - S_D Strouhal number based on f_D, - S_U Strouhal number based on f_u, - t time - u fluctuating component of instantaneous streamwise velocity - u rms of streamwise fluctuating velocity - u rms of streamwise fluctuating velocity upstream of cylinder - U mean streamwise velocity - U mean stream velocity upstream of cylinder - x streamwise distance measured from axis of cylinder - y transverse distance measured from axis of cylinder - z spanwise distance measured from floor of test section - v kinematic viscosity of air - density of air - time lag in cross-correlation function - _D normalized spectrum of fluctuating drag - _L normalized spectrum of fluctuating lift - _U normalized spectrum of fluctuating streamwise velocity